17.5, if both were the same difficulty homework for "Monie".
cone shaped storage container holds a photographic chemical. if the container is 60 cm wide and 20 cm high how many liters does it hold if 1 liter equal 1000cm3
Types of discontinuities
Identify and Classify the discontinuities in the function, please.
A function f(x) = (x⁴ - 5x² + 4) / (x² + x - 2) is discontinuous at x = 1 and x = -2. And it is a removable discontinuity.
Consider function f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)
We factorise denominator as,
x² + x - 2
= x² + 2x - x - 2
= x(x + 2) - 1(x + 2)
= (x + 2)(x - 1)
So, the function f(x) becomes,
f(x) = (x⁴ - 5x² + 4) / ((x + 2)(x - 1))
A function f(x) is discontinuous when the denominator of f(x) is zero.
i.e., (x + 2)(x - 1) = 0
i.e., x = 1 or x = -2
Also, the factors of the polynomial x⁴ - 5x² + 4 are (x - 2), (x + 2), (x - 1) and (x + 1)
We can write function f(x) as,
f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)
f(x) = ((x - 2) (x + 2) (x - 1) (x + 1)) / ((x + 2)(x - 1))
f(x) = (x - 2)(x + 1)
Now, the function f(x) is continuous.
Therefore, the type of discontinuity is removable discontinuity.
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What are the domain and range of the piecewise function
The domain of the function is, (-4, +∞) - {6}
And the range of the function is, R - [-2,0).
Since, The domain of a function is the set values of x for which the function is defined.
And, The range of a function is the set values of y for which the function is defined.
As we can see that the graph of the function can be defined everywhere except on 6 at the x-axis, and between 0 to -2 on the y-axis. therefore,
Domain = (-4, +∞) - {6}
Range = R - [-2,0)
Hence, the domain of the function is (-4, +∞) - {6} and the range of the function is R - [-2,0).
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if the angels of a quadrilateral are x, 2x and 3x. what is the value of x.
calculate the size of the largest angel.
Answer:
Step-by-step explanation:
The sum of angles in a quadrilateral is 360 degrees. So, we have:
x + 2x + 3x + fourth angle = 360
6x + fourth angle = 360
fourth angle = 360 - 6x
To find the value of x, we can use the fact that the angles in a quadrilateral add up to 360 degrees:
x + 2x + 3x + (360 - 6x) = 360
6x + 360 - 6x = 360
360 = 360
This equation is true for any value of x, so we cannot solve for x.
To find the size of the largest angle, we can substitute any value of x into the expression for the fourth angle and then find the largest of the four angles. For example, if we choose x = 30, then the angles are:
x = 30 degrees
2x = 60 degrees
3x = 90 degrees
fourth angle = 360 - (x + 2x + 3x) = 180 degrees
So the largest angle is 180 degrees.
find the equation in standard form for an ellipse whose Foci is (0,3) and (0,-3) with a major axis, length 10
Use the derivative (x-3)(x+1)(x+4)
to determine the local maxima and minima of f and the intervals of increase and decrease.
The local maximum of f is at (-5/3, 128/27), and the local minimum is at (4/3, -64/27).
To find the neighborhood maxima and minima of the capability f(x) = (x-3)(x+1)(x+4), we really want to take its subordinate:
f'(x) = (x+1)(x+4) + (x-3)(x+4) + (x-3)(x+1)
f'(x) = [tex]3x^2 + 6x - 20[/tex]
Setting f'(x) equivalent to nothing and settling for x, we get:
[tex]3x^2 + 6x - 20 = 0x^2 + 2x - 20/3 = 0(x+5/3)(x-4/3) = 0[/tex]
Thusly, the basic focuses are x=-5/3 and x=4/3.
To decide the time periods and diminishing, we can utilize the principal subsidiary test. Since f'(x) is a quadratic capability with a positive driving coefficient, it is dependably certain for x < - 5/3 and x > 4/3, and consistently negative for - 5/3 < x < 4/3.
Thusly, f(x) is expanding on the spans (- ∞, - 5/3) and (4/3, ∞), and diminishing on the stretch (- 5/3, 4/3).
To find the nearby maxima and minima, we can utilize the subsequent subsidiary test. Taking the subordinate of f'(x), we get:
f''(x) = 6x + 6
Subbing x=-5/3 and x=4/3, we get:
f''(- 5/3) = - 2 < 0, so f has a neighborhood greatest at x=-5/3.
f''(4/3) = 10 > 0, so f has a neighborhood least at x=4/3.
Thusly, the neighborhood limit of f is at (- 5/3, 128/27), and the nearby least is at (4/3, - 64/27).
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Please Help College Algebra
An equation for the line that passes through (-14, 14) and whose slope is undefined is x = -14.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (-14, 14) and an undefined slope, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 14 = undefined(x - (-14))
y - 14 = undefined(x + 14)
x = -14
In conclusion, the equation of a line that has an undefined slope represents a vertical line that crosses the x-axis only i.e x = -14.
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A sequence is defined by the function A(n) =8+ (n -1)(-4).
Which term, n, would result in A(n) = -172?
A) 44
B) 46
C)692
D)700
Answer:
B. 46.
Step-by-step explanation:
First we set up the equation A(n)=-172 and substitute the given equation for A(n), giving us -172=8+(n-1)(-4). Simplifying, we get -180=(-4n+12), or -4n=-192, or n=48. However, n represents the number of terms in the sequence, and since the sequence starts with n=1, we need to subtract 1 from our answer to get the term number corresponding to A(n)=-172. Therefore, the answer is B) 46.
plsss explain nd i’ll give brainliest answer
Answer: 118
Step-by-step explanation:
Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.
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please help i don’t understand
By completing squares, we can rewrite the quadratic equation as:
(x + 9)^2 = -9
How to complete squares?Remember the perfect square trinomial:
(a + b)^2 = a^2 + 2ab + b^2
Here we have the quadratic equation:
x^2 + 103 = -18x + 13
We can rewrite this as:
x^2 + 18x = 13 - 103
x^2 + 18x = -90
x^2 + 2*9*x = -90
We can add 9^2 and subtract 9^2 to get:
x^2 + 2*9*x + 9^2 - 9^2= -90
(x^2 + 2*9*x + 9^2) - 9^2= -90
(x + 9)^2 - 81 = -90
(x + 9)^2 = -90 + 81
(x + 9)^2 = -9
That is the equation we wanted to get.
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The organizer of a conference is selecting workshops to include. She will select from 10 workshops about genetics and 7 workshops about ethics. In how many
ways can she select 9 workshops if more than 6 must be about genetics?
What is the square root of 144?
Answer:
12
Step-by-step explanation:
The square root of 144 is 12. This is because when a number is squared, it means it is multiplied by itself. So, 12 multiplied by 12 is equal to 144. Therefore, the square root of 144 is the value that, when multiplied by itself, gives the result of 144. This value is 12. The square root of 144 is also a perfect square, which means it is a whole number that can be generated by multiplying two equal integers.
Steven and rebecca ran a race. Rebecca ran 3 times across the center of a circle with the diameter of 40. Steve ran ones around the circle. Who ran futher? By how much did they run futher by?
Steven ran more distance, and the difference is 5.6 units.
Who ran further and by how much?Rebbeca ran 3 times across the center of a circle whose diameter is 40 units, then the distance that she ran is 3 times that:
distance for Rebbeca = 40*3 = 120 units.
While Steven ran one time across the circumference, remember that the circumference is 3.14 times the diameter, so the distance that he ran is:
Distance for Steven = 3.14*40 = 125.6 units.
So Steven ran more, and the difference is:
125.6 - 120 = 5.6 units.
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Ron took 1 1/2 hours to drive to his office. His office was 120 km away from his house. Find his
driving speed.
Answer:
80 miles per hour.
Step-by-step explanation:
120 - 80 = 40 Because 40 is half than 80.
i need help with this please
If you choose the baseball workshop, you will need to know the kind of beverage that would be better for the participants after playing baseball, and if we ask participants it is likely they choose water or soda.
What do we know?Information about the workshop is limited; however, it is likely the participants have to play baseball and they will need to drink and eat something after this.
What do we want to know?We want to know the beverage and snack that would be better for hydration. Moreover, it can be expected the participants choose common options such as soda or water.
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Se decided to bike from his home to the library to retum some books. El bied
3
home to get itt. After getting the book from home, he biked to the library. What
the total distance, in milles. El had hiked when he finally reached the library
The total distance El had biked when he finally reached the library is 119/20 miles
Given that Eli biked for [tex]1\frac{1}{10}[/tex] miles two times extra as he missed a book at home.
The distance between the Elis house and library is [tex]3\frac{3}{4}[/tex] miles
We have to find the total distance Eli biked
Total distance = [tex]1\frac{1}{10} +1\frac{1}{10} +3\frac{3}{4}[/tex]
=11/10+11/10+15/4
20 is LCM of 10, 10 and 4
= 22+22+75/20
=119/20 miles
Hence, the total distance El had biked when he finally reached the library is 119/20 miles
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A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is:
The ratio of the cost price and the printed price of the book is 1.2444.
We have,
Let's assume the printed price of the book = P.
As per the problem, the shopkeeper is selling the book at a discount of 10% on the printed price. So the selling price of the book.
= (P - 0.1P)
= 0.9P.
The shopkeeper earns a profit of 12% on selling the book.
So, the selling price of the book is also 112% of the cost price.
That is,
0.9P = 1.12C
where C is the cost price of the book.
Now, let's find the ratio of the cost price and the printed price of the book:
C/P
= (C/0.9P)/(P/0.9P)
= 1.12/0.9
= 1.2444
Therefore,
The ratio of the cost price and the printed price of the book is 1.2444.
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Could anyone help me with this stat question?
The value of test statistics is -0.87.
We have,
n=25, mean= 24.4, s=9.2 and a=.05
As t = (x - [tex]\mu[/tex])/(s/√(n))
t = (24.4 - 26)/(9.2/√(25))
t = -0.8695652173913
t = -0.87
The sample size is n = 25, so df= 25 - 1= 24
So, the probabilities for the one tailed test are 0.20 and 0.15 respectively.
The p-value is between 0.15 and 0.20
The p-value is not less than α.
So, we can't reject the null hypothesis H0
We fail to reject the null hypothesis H0
Thus, the mean age of the prison population in cone city is 26 years.
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A baseball team's cap is selected from 3 different colors, 2 different clasps, and 4 different locations for the team logo. A decision is made not to include or not to include reflective piping.
The calculated value of the number of different outcomes in the sample space is 24
Calculating the number of different outcomes in the sample spaceFrom the question, we have the following parameters that can be used in our computation:
3 different colors, 2 different clasps, 4 different locationsUsing the above as a guide, we have the following:
Colors = 3
Clasps = 2
Locations = 4
So, we have
Outcomes = Colors * Clasps * Locations
Substitute the known values in the above equation, so, we have the following representation
Outcomes = 3 *2 * 4
Evaluate
Outcomes = 24
Hence, the number of different outcomes in the sample space is 24
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If we set α=0.01, what is the probability that we reject the null hypothesis when it was in fact true?
The probability is  _____
The probability by the given data is 1%.
We are given that;
set α=0.01
Now,
The probability of making a type I error is the significance level, or alpha (α), which is the threshold we set for rejecting the null hypothesis124. It is also known as the false positive rate3.
If we set α=0.01, it means that we are willing to accept a 1% chance of making a type I error. Hence, the probability that we reject the null hypothesis when it was in fact true is 0.01 or 1%.
Therefore, by probability the answer will be 1%.
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Heather and Cindy are playing “Guess My Shape.”
Heather has to describe a shape to Cindy accurately enough so that Cindy can draw it without ever seeing the shape.
Heather gives Cindy these clues:
Clue #1: The shape is similar to a rectangle with a base of 7cm and a height of 4cm.
Clue #2: The shape is five times larger than the shape it is similar to.
What are the dimensions of the new shape?
Answer:
The new shape has a base of 35 cm and a height of 20 cm.
Step-by-step explanation:
Since the shape is five times larger than the shape it is similar to, we can simply multiply everything by 5.
7×5=35
4x5=20
The new shape has a base of 35 cm and a height of 20 cm.
Hope this helps (and is correct)! Good luck on your homework!
what is the missing vaule of x on the diagram below
The measure of the missing vaule of x in the diagram is 43
What is the missing vaule of x in the diagramFrom the question, we have the following parameters that can be used in our computation:
The circle
Using the theorem of sum of angles on a circumference, we have
2x + 122 + 152 = 360
Evaluating the like terms, we have
2x = 360 - (122 + 152)
So, we have
2x = 86
Divide by 2
x = 43
Hence, the missing vaule of x in the diagram is 43
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Evaluate the expression. C(11, 0)
The value of C(11, 0) is 1.
We have to find C(11, 0)
Using the definition of Combination
C(n, r) = n!/ r1 (n-r)!
Here, n =11 and r= 0
So, C( 11, 0)
= 11! / 0! (11-0)!
= 11! / 1 x 11!
= 1
Thus, the value of C(11, 0) is 1.
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What is $2.50 divided by 10
Answer:
answer is 0.25
Step-by-step explanation:
2.50/10
there is only one zero in 10 so we move the decimal one digit towards left.
which then the decimal ends up in front of 2.
What is the answer to this equation need this soon!!!
The measures of the angles add up to 180°, using that we can see that x = 10.
How to find the value of x?Here we can see that the two vertical lines are parallel, thus, the angles in both intersections are equal.
Now, notice that the 75° angle would be an adjacent angle to (11x - 5)°, then their measures add up to 180°, then we can write:
75° + (11x - 5)° = 180°
We can solve that for x.
75 + 11x - 5 = 180°
70 + 11x = 180
11x = 180 - 70 = 110
x = 110/11
x = 10
That is the value of x.
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2. Over the course of five weekdays, one mining stock on the Toronto Stock Exchange (TSX) closed
at $4.28 on Monday, closed higher at $5.17 on Tuesday, finished Wednesday at $4.79, and shot up
to close at $7.15 on Thursday, only to finish the week at $6.40.
a) What is the net change in the value of this stock for the week?
b) Determine the total change in the value of the stock.
Net change is the difference
between a prior trading
period's closing price and the
current trading period's
closing price.
The net change in the value of this stock for the week is $2.12.
The total change in the value of the stock is $4.38.
We have,
a)
The net change in the value of the stock for the week is the difference between the closing price on Monday and the closing price on Friday.
Net change expression.
= $6.40 - $4.28
= $2.12
b)
The total change in the value of the stock is the sum of the absolute changes from day to day.
Total change expression.
= |$5.17 - $4.28| + |$4.79 - $5.17| + |$7.15 - $4.79| + |$6.40 - $7.15|
= $0.89 + $0.38 + $2.36 + $0.75 = $4.38
Thus,
The net change in the value of this stock for the week is $2.12.
The total change in the value of the stock is $4.38.
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Mr.A sells watches. He is paid a monthly commission. received 21% of his first $1,500 in sales and 14% of the balance of his sales. Last month he sold $2,233 worth of watches. How much commission did he earn last month? and show your work.
The amount of commission Mr. A received last month is C = $ 417.62
Given data ,
Let the amount of commission earned be C
Now , the equation is
The first $1,500 in sales are eligible for a commission rate of 21%, so the commission on this portion of his sales is:
0.21 x $1,500 = $315
The remaining portion of his sales is:
$2,233 - $1,500 = $733
This amount is eligible for a commission rate of 14%, so the commission on this portion of his sales is
On simplifying the equation , we get
0.14 x $733 = $102.62
To find Mr. A's total commission, we add the commission on the first $1,500 to the commission on the remaining $733
$315 + $102.62 = $417.62
Hence , Mr. A earned a commission of $417.62 last month
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On Monday, one share of a certain stock costs $41.45. On Tuesday, the cost goes up by $0.58. It goes down by $0.26 on both Wednesday and Thursday. On Friday, it goes down by $0.06. Write an expression to represent the cost of one share of the stock on Friday. Then evaluate the expression to find the cost on Friday.
Answer:
The cost of one share of the stock on Friday is $41.45
Step-by-step explanation:
The initial cost of one share of the stock on Monday is $41.45.
On Tuesday, the cost goes up by $0.58, so the cost becomes:
$41.45 + $0.58 = $42.03
On Wednesday, the cost goes down by $0.26, so the cost becomes:
$42.03 - $0.26 = $41.77
On Thursday, the cost also goes down by $0.26, so the cost becomes:
$41.77 - $0.26 = $41.51
Finally, on Friday, the cost goes down by $0.06.
So the expression to represent the cost of one share of the stock on Friday is:
$41.51 - $0.06
To evaluate this expression, we simply subtract $0.06 from $41.51:
$41.51 - $0.06 = $41.45
Therefore, the cost of one share of the stock on Friday is $41.45
Helppp fastttttt!!!!!!
Answer:
its 15.5 m
Step-by-step explanation:
The distance between City A and City B is 250 miles. A length of 1.7 feet represents this distance on a certain wall map. City C and City D are 4.42 feet apart on this map. What is the actual distance between City C and City D?
The actual distance between City C and City D is approximately 647.06 miles.
We can use the given information to determine the scale of the map, which relates distances on the map to actual distances in the real world. Let x be the actual distance between City C and City D in miles. According to the map, the distance between City C and City D is represented by 4.42 feet. We can write this relationship as:
250 miles / 1.7 feet = x miles / 4.42 feet
Solving for x, we get:
x = (4.42 feet * 250 miles) / 1.7 feet = 647.06 miles
The key concept used in this problem is the idea of scale. Maps are often drawn to a specific scale, which allows us to relate distances on the map to actual distances in the real world. In this case, we used the scale of the map to convert the distance between City C and City D on the map (measured in feet) to the actual distance between the cities (measured in miles).
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